Question

12) A radio transmission tower is 170 feet tall. How long should a guy wire be if it is to be attached 15 feet from the top and is to make an angle of 30° with the ground? Give your answer to the nearest tenth of a foot.
13) A building 230 feet tall casts a 100 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.)

Answer 1

The length of guy wire needed to make an angle of 30° with the ground is 310 feet. The angle between the end of the shadow and the vertical side of the building is 23°

What is trigonometric ratio?

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

a) Let l represent the length of the guy wire.

sin(30) = (170 - 15) / l

l = 310 feet

b) Let Ф represent the angle, hence:

tanФ = 100/230

Ф = 23°

The length of guy wire needed to make an angle of 30° with the ground is 310 feet. The angle between the end of the shadow and the vertical side of the building is 23°

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